I completely agree with the instructional moves here and how presenting a non-routine task like match the solution to the original equation will produce much richer and more diverse thinking from students. I think what is sometimes lost in these experiences (especially when tech is involved) is all the minute teacher moves needed to maximize this instructional move for student learning. For example:
- having students tent laptops after their initial exploration before beginning a whole class discussion
- sequencing student ideas so that they build toward a common understanding (also requires monitoring and listening while students discuss with partners)
- asking questions that elicit student thinking that is aligned to a main idea (these can be somewhat pre-planned based on the content)
- teaching students norms for how to respond to one another’s ideas (ask a follow-up question, build on an idea, disagree with an idea etc.)
- reinforcing norms that create a safe space for sharing ideas such as: “disagree with ideas, not people”
This is not an exhaustive list. Sometimes people mistakenly assume putting the tech activity in front of students is the teaching and don’t understand why students aren’t able to arrive at a common conceptual understanding from it (this can also happen with non-tech related tasks). The more diverse the student thinking related to a task, the greater the need for strong facilitation of discussion to bridge to common conceptual understanding IMO.
Your talk at AIRShow last year was spectacular! Amongst the swirling sea of "AI Hype", you shared the most teacher-centered presentation. Very excited to hear another one this year!
Great read, as always. Matchy Match sounds great! This modeling and reasoning with tape-diagrams can then be practiced, built upon, and assessed on paper using multiple-choice, select-all, T/F, agree/disagree, and explain-why type questions.
AIR sounds interesting and definitely something I'll listen to.
Elizabeth's highlighted comment reminded me that AI tools in education need to improve and strengthen a teacher's content knowledge and expertise - NOT diminish it. The productive struggle of novice teachers around content is just as important, and if AI reduces that, then teachers grow at a slower rate.
Dylan's comment about completely shutting Chromebooks to have a discussion is expert-level advice, and interesting to think about.
Hahaha Unbounded Academy. I certainly want to hear anything the Ed-Surge co-founder has to say. The application to the Stanford lab is exciting!
Having kids be part of the curriculum works beyond math.
In fact having participants being part of the curriculum works as well for adult learning. Wait, what am I talking about, the purpose of professional development isn't to engage the learners, it's to bore them to the point that they have this uncontrollable urge to get back into their own classrooms, right?
Pity Musk Jd Vance and Trump have no facility for math, math conversations beyond "your less" "is my more" But to this work of yours BRAVO. If teachers can did deep into the democratic nature of your math conversations. There is hope for us. A Buzzing classroom with student problem solving is such a balm for a teachers soul and such a gift for students.
I teach a class where the very first lesson is on understanding big numbers, how the difference between a million and a billion isn't just one letter. Then I see in the news that Elon Musk was representing an $8 million cut as an $8 billion cut.
Oh this reminds me of low fidelity design, typically used in software prototyping ... it feels so much more inviting having hand writing, squiggly lines, intentional mistakes :)
As always - lots to think about in this email/post. I appreciate your thoughts on AI and the resources you've flagged for us to peruse.
Love the idea of Matchy Match - leveraging student work to launch discussions rather than teacher or curriculum-produced content. I agree with Kristen Smith (below) that I'd also like to see some articulation of how that can happen - to expand on the designs for interaction between students and content. I can (very easily) envision wedding Matchy Match to the Connecting Representations Instructional Routine :)
Look forward to hearing this year's AIR talk and whether or not it gets you: A. uninvited B. escorted out or C. invited back.
> I can (very easily) envision wedding Matchy Match to the Connecting Representations Instructional Routine :)
Same! I'm wondering if technology can improve the likelihood of a teacher successfully enacting a routine. If successfully enacting routines requires several jumps—from reading about them on the page to using them to interpret student thinking to to saying stuff out loud in class—I'm wondering where technology can make those jumps shorter & easier. Put another way—if a computer had assembled that Matchy Match screen, what is gained / lost.
One question: If you're showing student work, are you only showing correct work?
And one more: If you wanted to add in some incorrect work, how would you do that? I assume you wouldn't want to show incorrect work from a student in the class, perhaps say "Some of these come from another class"?
One of the students in the second example WAS wrong. I didn't attribute the answer to the student by name. I try to inoculate any stigma by treating all of the answers as serious and interesting, for example by saying, "What equation did this student ACTUALLY describe?"
What do you mean by teacher pedagogies and beliefs through digital tools? Your writing suggests that it is difficult to change students using digital tools,that is, ai. Why do you think teachers are different than students. I think belief change can best occur when it is up close and personal
Our tools are changing us just as much as we change the world through our tools. Our tools shape our bodies, our minds, and our beliefs. The same is true of digital tools. AI chatbots are a poor tool for learning but that doesn't mean the same is true for EVERY tool and EVERY purpose. And, yes, I agree that relationship is a powerful accelerant for change.
I want to push back on AI being a poor tool for learning. I know there are places, and types of people, for whom it is an amazing tool. But like all tools they need to be used for the right task in the right way. I am good with screwdrivers and hammers but figuring out the use cases and how to use AI in those situations is still an open question for me. However, I very much appreciate Dan’s analysis and critiques! I am seeing lots of hype that this “hammer” is the tool above all others. Ok, maybe not hammer because I definitely use that one a lot!
The issue for me is how one goes about changing teacher beliefs about helping students learn (I avoid the word “teaching”) remotely and not having access to their classroom. I have tried having the teacher record a video of the classroom for discussion but so far that has, for me, not been a successful way to impact the teachers beliefs. Perhaps the problem is these of science teachers who understand some of the science. I have found that the more content knowledge the teacher believes they have, the harder it is to change what happens in the classroom. Does that happen in mathematics also?
I believe you when you describe how the classroom buzzed in response to that question, and when you talk about the rich student thinking in the Desmos curriculum. I see that from a majority of my students when I use Desmos activities.
My concern is about the growing minority who seem to be heading the opposite direction, who have built up really negative habits around tech use. I worry that it's really easy to look at the success stories, and sweep the growing issues under the rug. Do you have any data on that? I realize it's a hard thing to gather data on. But that issue seems kindof orthogonal to what you're describing in the post.
• I think this is a question that's really hard to study.
• I think if students are going to get better at using tech as a learning resource that probably needs to happen in the spaces where they use learning resources. I feel fine if someone says, "helping students get better at using tech as a learning resource is not my bag." Paper has a fine track record.
• Students have always experienced every resource & medium differentially. The best things I think I can do for struggling students transcend the medium—provide support and accountability. I have taught in this classroom maybe four times this year and I'm starting to understand which students need to hear me say, "Hey I'm really interested in what you'll say here and I'm coming back to you after."
I completely agree with the instructional moves here and how presenting a non-routine task like match the solution to the original equation will produce much richer and more diverse thinking from students. I think what is sometimes lost in these experiences (especially when tech is involved) is all the minute teacher moves needed to maximize this instructional move for student learning. For example:
- having students tent laptops after their initial exploration before beginning a whole class discussion
- sequencing student ideas so that they build toward a common understanding (also requires monitoring and listening while students discuss with partners)
- asking questions that elicit student thinking that is aligned to a main idea (these can be somewhat pre-planned based on the content)
- teaching students norms for how to respond to one another’s ideas (ask a follow-up question, build on an idea, disagree with an idea etc.)
- reinforcing norms that create a safe space for sharing ideas such as: “disagree with ideas, not people”
This is not an exhaustive list. Sometimes people mistakenly assume putting the tech activity in front of students is the teaching and don’t understand why students aren’t able to arrive at a common conceptual understanding from it (this can also happen with non-tech related tasks). The more diverse the student thinking related to a task, the greater the need for strong facilitation of discussion to bridge to common conceptual understanding IMO.
Great list. Exhausting while not exhaustive. The description of the norms is particularly helpful, I think.
Your talk at AIRShow last year was spectacular! Amongst the swirling sea of "AI Hype", you shared the most teacher-centered presentation. Very excited to hear another one this year!
Great read, as always. Matchy Match sounds great! This modeling and reasoning with tape-diagrams can then be practiced, built upon, and assessed on paper using multiple-choice, select-all, T/F, agree/disagree, and explain-why type questions.
AIR sounds interesting and definitely something I'll listen to.
Elizabeth's highlighted comment reminded me that AI tools in education need to improve and strengthen a teacher's content knowledge and expertise - NOT diminish it. The productive struggle of novice teachers around content is just as important, and if AI reduces that, then teachers grow at a slower rate.
Dylan's comment about completely shutting Chromebooks to have a discussion is expert-level advice, and interesting to think about.
Hahaha Unbounded Academy. I certainly want to hear anything the Ed-Surge co-founder has to say. The application to the Stanford lab is exciting!
Having kids be part of the curriculum works beyond math.
In fact having participants being part of the curriculum works as well for adult learning. Wait, what am I talking about, the purpose of professional development isn't to engage the learners, it's to bore them to the point that they have this uncontrollable urge to get back into their own classrooms, right?
Pity Musk Jd Vance and Trump have no facility for math, math conversations beyond "your less" "is my more" But to this work of yours BRAVO. If teachers can did deep into the democratic nature of your math conversations. There is hope for us. A Buzzing classroom with student problem solving is such a balm for a teachers soul and such a gift for students.
I teach a class where the very first lesson is on understanding big numbers, how the difference between a million and a billion isn't just one letter. Then I see in the news that Elon Musk was representing an $8 million cut as an $8 billion cut.
Oh this reminds me of low fidelity design, typically used in software prototyping ... it feels so much more inviting having hand writing, squiggly lines, intentional mistakes :)
https://www.interaction-design.org/literature/article/prototyping-learn-eight-common-methods-and-best-practices
As always - lots to think about in this email/post. I appreciate your thoughts on AI and the resources you've flagged for us to peruse.
Love the idea of Matchy Match - leveraging student work to launch discussions rather than teacher or curriculum-produced content. I agree with Kristen Smith (below) that I'd also like to see some articulation of how that can happen - to expand on the designs for interaction between students and content. I can (very easily) envision wedding Matchy Match to the Connecting Representations Instructional Routine :)
Look forward to hearing this year's AIR talk and whether or not it gets you: A. uninvited B. escorted out or C. invited back.
Thanks for pushing my thinking here, Amy.
> I can (very easily) envision wedding Matchy Match to the Connecting Representations Instructional Routine :)
Same! I'm wondering if technology can improve the likelihood of a teacher successfully enacting a routine. If successfully enacting routines requires several jumps—from reading about them on the page to using them to interpret student thinking to to saying stuff out loud in class—I'm wondering where technology can make those jumps shorter & easier. Put another way—if a computer had assembled that Matchy Match screen, what is gained / lost.
The animation of the two approaches for using the tape diagrams was great for me. Such a nice use of tech to illuminate an idea👍
One question: If you're showing student work, are you only showing correct work?
And one more: If you wanted to add in some incorrect work, how would you do that? I assume you wouldn't want to show incorrect work from a student in the class, perhaps say "Some of these come from another class"?
One of the students in the second example WAS wrong. I didn't attribute the answer to the student by name. I try to inoculate any stigma by treating all of the answers as serious and interesting, for example by saying, "What equation did this student ACTUALLY describe?"
What do you mean by teacher pedagogies and beliefs through digital tools? Your writing suggests that it is difficult to change students using digital tools,that is, ai. Why do you think teachers are different than students. I think belief change can best occur when it is up close and personal
Best
Joe
Our tools are changing us just as much as we change the world through our tools. Our tools shape our bodies, our minds, and our beliefs. The same is true of digital tools. AI chatbots are a poor tool for learning but that doesn't mean the same is true for EVERY tool and EVERY purpose. And, yes, I agree that relationship is a powerful accelerant for change.
I want to push back on AI being a poor tool for learning. I know there are places, and types of people, for whom it is an amazing tool. But like all tools they need to be used for the right task in the right way. I am good with screwdrivers and hammers but figuring out the use cases and how to use AI in those situations is still an open question for me. However, I very much appreciate Dan’s analysis and critiques! I am seeing lots of hype that this “hammer” is the tool above all others. Ok, maybe not hammer because I definitely use that one a lot!
The issue for me is how one goes about changing teacher beliefs about helping students learn (I avoid the word “teaching”) remotely and not having access to their classroom. I have tried having the teacher record a video of the classroom for discussion but so far that has, for me, not been a successful way to impact the teachers beliefs. Perhaps the problem is these of science teachers who understand some of the science. I have found that the more content knowledge the teacher believes they have, the harder it is to change what happens in the classroom. Does that happen in mathematics also?
I believe you when you describe how the classroom buzzed in response to that question, and when you talk about the rich student thinking in the Desmos curriculum. I see that from a majority of my students when I use Desmos activities.
My concern is about the growing minority who seem to be heading the opposite direction, who have built up really negative habits around tech use. I worry that it's really easy to look at the success stories, and sweep the growing issues under the rug. Do you have any data on that? I realize it's a hard thing to gather data on. But that issue seems kindof orthogonal to what you're describing in the post.
A few thoughts:
• Yeah, I share the worry.
• I think this is a question that's really hard to study.
• I think if students are going to get better at using tech as a learning resource that probably needs to happen in the spaces where they use learning resources. I feel fine if someone says, "helping students get better at using tech as a learning resource is not my bag." Paper has a fine track record.
• Students have always experienced every resource & medium differentially. The best things I think I can do for struggling students transcend the medium—provide support and accountability. I have taught in this classroom maybe four times this year and I'm starting to understand which students need to hear me say, "Hey I'm really interested in what you'll say here and I'm coming back to you after."